Evaluating real estate properties

ABSTRACT

The present invention is an improved system and method for analyzing multiple real estate properties. The system includes a pool of properties that are searched based on user-defined search criteria. The system identifies comparison properties from the search pool. The comparison properties include attributes that match or are a near match to the search criteria. The system compares each of the comparison properties to at least one average value and demonstrably depicts the comparison to the user.

BACKGROUND OF THE INVENTION

The present invention generally relates to real estate evaluations, andmore particularly to identifying an optimal real estate property amongalternatives.

Generally, real estate properties are offered for sale by sellersthrough real estate brokers. Typically, the real estate broker preparesinformation about the property using a form developed by the brokeragecompany or by a local multiple listing service that describes theproperty in a prescribed way. This description is generally referred toas a listing. Listings are customarily stored in a search pool of acomputerized system that maintains information regarding properties forsale. Several of these computer systems include techniques by whichlisting information is retrieved from the search pool by price, type,property address or zip code. Typically, these systems sort the searchpool of properties and present properties within a defined range basedon a predefined sort selection.

For example, in U.S. Pat. No. 5,754,850 to Jansen, a method andapparatus is provided for a search system based in software running on apersonal computer. In the search system, selection features are selectedand a search based upon these search features is performed. Itemsneither satisfying or closely satisfying the search features of thesearch are eliminated from the search.

Although the above systems identify real estate properties that meetpredefined criteria, there is an increasing need for improved searchingtechniques in markets where there are large populations of availableproperties for sale. For example, computer systems of the prior artusing predefined sort selection criteria can present enormous quantitiesof properties based on the number of available properties for sale. Realestate salespeople are finding it increasingly difficult to discriminatethe total number of available properties for sale retrieved from thesesystems to effectively serve their customers.

More recently, to address this problem, real estate brokers have begunlimiting the population of available properties for sale by focusingtheir search on a small number of buildings where they can presentthemselves as a building specialist. Although this approach allows thebroker to develop a universe of alternative properties which are moremanageable, limiting the dimension of such searches does not effectivelyserve real estate customers. As such, an improved technique foranalyzing a large number of available real estate properties based onmultiple criteria is sorely needed.

SUMMARY OF THE INVENTION

Thus, the present invention is an improved system and method foranalyzing multiple real estate properties. The system includes a pool ofproperties that are searched based on user-defined search criteria. Thesystem identifies comparison properties from the search pool. Thecomparison properties include attributes that match or are a near matchto the search criteria. The system compares each of the comparisonproperties to at least one average value and demonstrably depicts thecomparison to the user.

Various aspects of the system relate to identifying, comparing, anddisplaying real estate properties.

For example, according to one aspect, a method of analyzing real estateproperty includes determining a plurality of search features associatedwith each property found in a search pool of properties, each of thesearch features having an attribute value associated therewith, andidentifying comparison properties from the search pool using at leastone of the search features. The method also includes determining atleast one average attribute value associated with the search featuresfor the comparison properties, comparing each of the attribute value foreach comparison property with an average attribute value, anddemonstrably depicting the comparison.

In one preferred embodiment, the method includes searching the pool andselecting comparison properties using an initial filtering criteriabased on at least one of the plurality of search features. Preferably,determining the initial filtering criteria includes determining a pricerange of purchase price. The method can also include determining anupper price value using a seller price, and determining a lower pricevalue using a purchase price.

The method includes comparing at least one attribute of the propertiesto at least one of the plurality of search features. The method can alsoinclude summing the attribute value of each comparison property, anddividing each of the sums by the total number of comparison properties.

For example, the search features can be selected from the groupconsisting of property type, purchase price, location, building type,light, space and cost. The method can also include displaying thecomparison in a grid or table, as well as evaluating the comparisonproperties using the comparison.

A system, as well as articles which include a machine-readable mediumstoring machine-readable instructions for implementing the varioustechniques, are disclosed. Details of various implementations arediscussed in greater detail below.

As a result of the invention, a real estate salesperson can defineseveral search criteria that more accurately reflect what buyers haveidentified as purchasing criteria.

Further benefits include an ability to filter a population ofalternative properties from a large potential universe of propertiesbased on the user-configurable search criteria. Another benefit is amethod for identifying comparative properties. For example, by averagingcharacteristics of a population of properties and then portraying eachindividual property against the averages, a salesperson can effectivelywork with a very large population of alternative properties and show acustomer how a specific property is superior to alternatives.

Other objects and features of the present invention will become apparentfrom the following detailed description considered in conjunction withthe accompanying drawings. It is to be understood, however, that thedrawings are designed as an illustration only and not as a definition ofthe limits of the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates a block diagram of a networked computer system foranalyzing real estate properties according to the present invention.

FIG. 2 is a flow chart of a method executed by the system of FIG. 1 toanalyze real estate properties according to the present invention.

FIG. 3 illustrates an example of establishing initial filtering criteriaaccording to the present invention.

FIG. 4 illustrates an example of filtering properties from a searchpool.

FIG. 5 illustrates an example of calculated averages associated withsearch criteria.

FIG. 6 illustrates an example of comparison properties displayedpictorially.

Like reference symbols in the various drawings indicate like elements.

DETAIL DESCRIPTION OF THE PREFERRED EMBODIMENTS

Referring to FIG. 1, in one preferred embodiment, a computer-basedsystem 10 that analyzes real estate properties is disclosed. The system10 includes a server 22 that analyzes real estate property informationin response to requests from access devices 12A-D. As shown in FIG. 1, auser using an access device 12A-D over a network 16 can access theserver 22 to request and receive the analyzed real estate propertyinformation.

In the embodiment shown in FIG. 1, each access device 12A-D isconfigured with a web browser 14A-D capable of requesting and displayingthe real estate property information. The access devices 12A-D caninclude a personal computer, a laptop computer, or otherelectronic-based device to access the server 22. Although only fouraccess devices are illustrated in FIG. 1, the system 10 can beconfigured to support various numbers of access devices.

Network 16 can include various devices such as servers, routers, andswitching elements that can be connected in an extranet, intranet orInternet configuration. In some implementations, the network 16 useswired communications to transfer information to and from the accessdevices 12A-D and the server 22. In other implementations, the network16 uses wireless communication protocols. In yet other implementations,the network 16 uses a combination of wired and wireless communicationprotocols.

Database 18 provides access to descriptive information relating to oneor more real estate properties and is accessible to the server 22. Inone preferred embodiment, the database 18 is a relational database thatmaintains real estate property information in a search pool 20. Inanother preferred embodiment, the database 18 is a directory server,such as a Lightweight Directory Access Protocol (‘LDAP’) server, thatmaintains real estate information in the search pool 20. In otherimplementations, the database 18 and search pool 20 are a configuredarea in the non-volatile memory 32 of the server 22 that maintains realestate property information. Of course, it will be appreciated by oneskilled in the art that the database 18 can also be accessed over thenetwork 16 and can be used to not only maintain real estate descriptiveinformation but can also be used to store calculated real estateinformation as described below.

As shown in FIG. 1, the server 22 includes a central processing unit(‘CPU’) 24, random access memory (‘RAM’) 26, non-volatile memory 32 andan input-output device 28, all of which are interconnected via a busline 30 and controlled by the CPU 24. The non-volatile memory 32 isconfigured to include a web server 34 to communicate with access devices12A-D, a selector module 36 to determine search features associated withproperty in the search pool 20, an analyze module 40 to identifycomparison properties from the search pool 20 and a display module 38 todisplay pictorially attributes of the comparison properties.

Web server 34 manages communications between the access devices 12A-Dand the server 22. Preferably, the web server 34 is configured to sendand receive information in the form of web pages to any of the browsers14A-D in response to a request. The web server 34 communicates with eachweb browser 14A-D and software modules 36, 38 and 40 using one or morecommunication protocols, such as HTTP (Hyper Text Markup Language). Inone preferred embodiment, for example, the web server 34 is configuredto include the Apache HTTP Server from the Apache Software Foundation.In another preferred embodiment, the web server 34 includes InternetInformation Services (IIS) from Microsoft Corporation. In yet anotherpreferred embodiment, the web server 34 includes the Sun Java System WebServer from Sun Microsystems.

Referring now to FIG. 2, a flow chart of a method executed by the systemof FIG. 1 to analyze real estate properties is disclosed. As shown inFIG. 2, first, the system 10 determines search features associated witheach search property in a search pool 42. Next, in one preferredembodiment, the system 10 determines an initial filtering criteria fromat least one the search features 44. Preferably, this includescalculating an upper price value using a seller price 46 and calculatinga lower price value using a purchase price 48. Next, the system 10selects filtered properties from the search pool using the filteringcriteria 50. The system 10 then selects comparison properties from thefiltered properties using the search features 52. Next, the system 10calculates an average value associated with search features using thecomparison property selection 54. In one preferred embodiment, thesystem 10 sums attribute values of each comparison property 56 and thendivides each of the sums by the total number of comparison propertiesselected 58. Next, the system 10 compares each attribute valueassociated with each comparison property to the calculated average valuefor each search feature 60. Finally, the system 10 displays thecomparison graphically in a grid or table format 62. Details of theabove described steps along with the software modules provided toexecute the same are discussed in further detail below.

Referring back to FIG. 1, the selector module 36 of the presentinvention determines the search features associated with real estateproperties in the search pool 20 in response to a request received fromthe one of the browsers 14A-D via the web server 34. For example, in onepreferred embodiment, the selector module 36 queries one or more tabledefinitions of the search pool 20 to determine available searchfeatures. Once the search features are retrieved, the selector module 36provides the search features to the access devices via the web server 34as user selectable search criteria. For example, in response to a userrequest from one of the access devices 12A-D, the selector module 36provides the following user selectable search features: property typee.g., single family, condominium, cooperative, business property, etc.,seller's asking price, preferred location, building type, light, space,and cost.

Preferably, the selector module 36 displays the property type andlocation search features of properties on a user selectable scale eachhaving attribute values ranging from 1 to 10. Similarly, the selectormodule 36 displays a lighting availability search feature forproperties. For example, in one preferred embodiment, the selectormodule 36 provides a user selectable scale having attribute valuesranging from 1 to 10 representing relative floor locations (e.g., 1^(st)floor, 5^(th) floor, 10^(th) floor, etc.) and grade for a predominantview available in any one particular room of a property.

The selector module 36 allows the user to quantify qualitativepreferences regarding “value rooms”. For example, in the context of anapartment search, the selector module 36 provides the user with spacesize choices for a living room, dining room and master bedroom. Theselector module 36 then quantifies the space in these rooms bycalculating an accumulated figure representing dimensions of the spacein the apartment. Preferably, the selector module 36 also allows theuser to select monthly carrying costs that include maintenance costs fora cooperative and a combination of common charges and real estate taxesfor condominiums.

In some preferred embodiments, the selector module 36 allows the user toidentify different ownership interests in real estate property. Forexample, in one preferred embodiment, the selector module 36 provides aconfigurable standard form of ownership consisting of a 25% equityinterest and a 75% financing option and portrays the relative downpayment of each property and associated monthly carrying costs includingdebt service.

In another preferred embodiment, the selector module 36 provides an airsearch feature representing the openness of a real estate property. Theselector module 36 determines values for the air search feature byconsidering ceiling heights and property layout. Preferably, theselector module 36 does not discriminate properties based on the airsearch feature but provides the same as a reference for the user duringfinal real estate property selection.

As discussed in connection with FIG. 2, the selector module 36 candetermine an initial filtering criteria from one or more of thedetermined search features and select properties from the search pool 20using the filtering criteria. The initial filtering criteria can be aprice range that is derived from a user purchase price.

For example, referring now to FIG. 3, the selector module 36 can firstdetermine an initial purchasing price 70 that is input by the user andthen vary that amount above the requested purchase price to model thefact that most purchasers and sellers of property are willing tonegotiate. The selector module 36 can vary the amount of negotiability72 given supply/demand factors at any given time based on user input.Next, the selector module 36 identifies a price point where there is alikelihood that a seller in the market can negotiate a deal with apurchaser given current market conditions. Preferably, the currentmarket conditions are input by the user. The selector module 36 thendetermines a range of prices between the purchaser's requested price 70and the calculated price point which represents a seller's price 74.Preferably, the seller price 74 is calculated by adding the amount ofnegotiability 72 to the purchaser's requested price 70. Next, theselector module 36 determines a price point below the purchaser'srequested price 70, hereinafter referred to as a “low-end extension”value 78 which represents unique opportunities that can exist in themarketplace below the purchaser's requested price 70. Next the selectormodule 36 identifies the dollar amount represented by the value of thelow-end extension 78 and the seller's asking price 74. By doubling thissum, the seller's asking price becomes an average point or benchmarkthat the analyze module 40 can compare each property to. Next, as shownin FIG. 3, the selector module 36 determines a low-end range 82representing values below the average point less the amount ofnegotiability 72 and a high-end range 84 representing values above theaverage point plus the amount of negotiability 72. Lastly, the selectormodule 36 combines the two ranges 82, 84 to form an initial filteringcriteria 80 and selects properties from the search pool 20 using thesame.

The analyze module 40 of the present invention identifies comparisonproperties from the search pool 20 using one or more user selectablesearch features, determines one or more average attribute valuesassociated with the comparison properties and compares each of theattribute values for each comparison property with one or more of thecalculated average attribute values. In one preferred embodiment, theanalyze module 40 rounds the calculated average attribute values to thenearest whole number. Of course, it will be appreciated by one skilledin the art that other rounding techniques can be utilized by the analyzemodule 40.

Preferably, the analyze module 40 is initiated in response to a requestreceived from one of the browsers 14A-D via the web server 34. Theanalyze module 40 may then select comparison properties from the searchpool using one or more of the user selectable search features. Althoughinitial filtering can decrease the number of available properties forcomparison, as discussed in connection with the selector module 36, thenumber of properties to be compared can still be large to evaluateefficiently. Advantageously, the analyze module 40 allows the user tofurther refine and filter properties based on any number of searchfeatures to obtain a population of comparison properties that the userdeems appropriate under the circumstances.

For example, referring now to FIG. 4, an example of filtration providedby the analyze module 40 is shown. In the FIG. 4 example, comparisonapartments are being filtered. The example assumes that a large numberof properties are already identified from the search pool 20 using apricing range of $475,000 to $725,000.

As shown in the FIG. 4 example, the space search feature is firstemployed as a main determinant for a user purchasing property. Theanalyze module 40 filters the selected properties 90 by requiring thatthe attribute value associated with the space feature of each propertyinclude dimensions substantially equivalent to 30×12 for a living roomand 16×11 for a master bedroom. Once the analyze module 40 completes thefiltration, the number of selected properties having those attributevalues are reported to the user via the web server 34. If the number ofselected properties remains too large, the user can request the analyzemodule 40 to apply additional filters as necessary to obtain amanageable number of comparison properties. For example, as shown inFIG. 4, a second filter representing light is selected by the user. Theanalyzer module 40 then filters the comparison apartments to eliminateall apartments below the 8^(th) floor 92 resulting in a remaining numberof properties for comparison 94.

As discussed in connection with FIG. 2, the analyzer module 40 canaverage the remaining population of comparison properties based on thesearch features. For example, referring now to FIG. 5, a sample ofcomparison properties 120 each having associated therewith an attributevalue associated with a search feature is shown. Preferably, as shown inFIG. 5, the search features include an address feature 96,location-grade feature 98, building-grade feature 100, light feature 106having both a floor indicator 102 and view grade 104, a space feature114 having a living room 108 and master bedroom feature 112, acalculated total space feature 112, asking price 116 and cost feature118.

The analyze module 40 sums each attribute value of each comparisonproperty 122 and divides each of the sums 122 by a total number ofcomparison properties to calculate average attribute values 124. Asmentioned previously and as shown in FIG. 5, the analyze module 40 alsocan include rounding techniques during calculation of average attributevalues.

Once the analyze module 40 calculates the average attribute values 124,the analyze module compares each comparison property attribute value toa respective calculated average attribute value and initiates thedisplay module 38 to display the same.

The display module 38 of the present invention demonstrably depicts thecomparison of selected property attributes to the calculated searchfeature averages generated by the analyze module 40 and sends the sameto the web server 34 for display on one or more browsers 14A-D.

For example, in one preferred embodiment, referring now to FIG. 6, thedisplay module 38 displays the comparison properties 120 in a table-likeform, such as a table or grid 121. Of course, it will be appreciated byone skilled in the art that other techniques for displaying thecomparison properties can be employed by the display module 38 and arewithin the scope of the present invention and claims. For example, inone preferred embodiment, the display module 38 depicts comparisonproperties using a bar chart. In another preferred embodiment, piecharts are used by the display module 38 to depict comparisonproperties.

Preferably, the display module 38 demonstrably depicts the comparison ofproperty attribute values to the calculated average attribute valuesusing symbols that indicate whether a particular property attributevalue is above, below, or substantially equal to the calculated averageattribute values. For example, as shown in FIG. 6, the display module 38uses symbols, such as ‘+’, ‘−’, and ‘=’, to demonstrably depict theproperty attribute comparisons.

For example, turning now to FIGS. 5 and 6, for one comparison property120E, the display module 38 displays a ‘+’ symbol 132 for the attributevalue associated with the grade feature. As shown in the FIG. 5 example,the calculated attribute average for the grade search feature is (7) andthe attribute value associated with property 120E for the grade featureis (9) indicating that property 120E's attribute value for grade isabove the average. Similarly, the display module 38 displays a ‘=’symbol 134 for the attribute value associated with the space searchfeature to indicate that the calculated search feature average of (598)is substantially the same as the attribute value associated withproperty 120E for space (595). Likewise, the display module 38 displaysa ‘−’ symbol 136 for the attribute value associated with the pricesearch feature as the price for property 120E (700K) exceeds thecalculated price average (597K) and is therefore less desirable.

Of course, it will be appreciated by one skilled in the art that othersymbols, graphics and animations can be used to show the attribute valuecomparisons. For example, in one preferred embodiment, upward anddownward directed arrows and dash lines are shown by the display module38 to pictorially display whether a particular property attribute valueis above, below, or substantially equal to calculated search featureaverages, respectively.

Advantageously, displaying the comparison property attribute valuespictorially allows a user of the system to develop a clearer portrayalof comparison properties and allows a user of the system discriminatebetween available properties efficiently.

A number of embodiments of the invention have been described.Nevertheless, it will be understood that various modifications can bemade without departing from the spirit and scope of the invention. Forexample, the modules described above can be organized or contained invarious ways, and can reside on multiple computers or a single computer.Also, the steps described above can be modified in various ways orperformed in a different order than described above, where appropriate.Accordingly, other embodiments are within the scope of the followingclaims.

What is claimed is:
 1. A method of analyzing real estate property, themethod comprising: determining a plurality of search features associatedwith each property found in a search pool of properties, each of saidsearch features having an attribute value associated therewith;identifying comparison properties from said search pool using at leastone of said search features; determining an average attribute valueassociated with a search feature for said comparison properties;comparing an attribute value of said search feature for each comparisonproperty to said average attribute value; and depicting demonstrablysaid comparison of said attribute value for each comparison property tosaid average attribute value with a symbol that indicates whether saidattribute value for each comparison property is one of above, below andsubstantially equal to said average attribute value.
 2. The method ofclaim 1, wherein identifying said comparison properties comprisessearching said pool and selecting properties using an initial filteringcriteria based on at least one of said plurality of search features. 3.The method of claim 2, wherein using said initial filtering criteriacomprises determining a price range of purchase price.
 4. The method ofclaim 3, wherein determining said price range comprises: determining anupper price value using a seller price; and determining a lower pricevalue using a purchase price.
 5. The method of claim 1, whereinsearching for comparison properties comprises comparing at least oneattribute of said properties to at least one of said plurality of searchfeatures.
 6. The method of claim 1, wherein determining said averageattribute value comprises: summing said attribute value of eachcomparison property into a sum; and dividing said sum by a total numberof comparison properties.
 7. The method of claim 6, comprising roundingsaid average attribute value.
 8. The method of claim 1, wherein saidplurality of search features are selected from the group consisting ofproperty type, purchase price, location, building type, light, space andcost.
 9. The method of claim 1, further comprising displaying saidcomparison in a grid.
 10. The method of claim 1, further comprisingdisplaying said comparison in at least one of a bar chart and pie chart.11. The method of claim 1, wherein depicting demonstrably saidcomparison comprises displaying the symbol selected from the groupconsisting essentially of ‘+’, ‘−’ and ‘=’ based on said comparison. 12.The method of claim 1, further comprising evaluating said comparisonproperties using said comparison.
 13. A system to analyze real estateproperty, the system comprising: a search pool coupled to a network, thesearch pool storing real estate property information; a service deliverydevice coupled to the network, the service delivery device including aprocessor and memory storing instructions that, in response to receivinga request for access to a service, cause the processor to: determine aplurality of search features associated with each property found in saidsearch pool of properties, each of said search features having anattribute value associated therewith; identify comparison propertiesfrom said search pool using at least one of said search features;determine an average attribute value associated with a search featurefor said comparison properties; compare an attribute value of saidsearch feature for each comparison property to said average attributevalue; and depict demonstrably said comparison of said attribute valuefor each comparison property to said average attribute value with asymbol that indicates whether said attribute value for each comparisonproperty is one of above, below and substantially equal to said averageattribute value.
 14. The system of claim 13, wherein the memory storesinstructions that, in response to receiving the request, cause theprocessor to search said pool and select properties using an initialfiltering criteria based on at least one of said plurality of searchfeatures.
 15. The system of claim 14, wherein the memory storesinstructions that, in response to receiving the request, cause theprocessor to determine a price range of purchase price.
 16. The systemof claim 15, wherein the memory stores instructions that, in response toreceiving the request, cause the processor to: determine an upper pricevalue using a seller price; and determine a lower price value using apurchase price.
 17. The system of claim 13, wherein the memory storesinstructions that, in response to receiving the request, cause theprocessor to compare at least one attribute of said properties to atleast one of said plurality of search features.
 18. The system of claim13, wherein the memory stores instructions that, in response toreceiving the request, cause the processor to: sum said attribute valueof each comparison property into a sum; and divide said sum by a totalnumber of comparison properties to determine said average attributevalue.
 19. The system of claim 18, wherein the memory storesinstructions that, in response to receiving the request, cause theprocessor to round said average attribute value.
 20. The system of claim13, wherein the memory stores instructions that, in response toreceiving the request, cause the processor to select from the groupconsisting of property type, purchase price, location, building type,light, space and cost.
 21. The system of claim 13, wherein the memorystores instructions that, in response to receiving the request, causethe processor to display said comparison in a grid.
 22. The system ofclaim 13, wherein the memory stores instructions that, in response toreceiving the request, cause the processor to display said comparison inat least one of a bar chart and pie chart.
 23. The system of claim 13,wherein the memory stores instructions that, in response to receivingthe request, cause the processor to display the symbol selected from thegroup consisting essentially of ‘+’, ‘−’ and ‘=’ based on saidcomparison.
 24. An article comprising a machine-readable medium storingmachine-readable instructions that, when applied to the machine, causethe machine to: determine a plurality of search features associated witheach property found in said search pool of properties, each of saidsearch features having an attribute value associated therewith; identifycomparison properties from said search pool using at least one of saidsearch features; determine an average attribute value associated with asearch feature for said comparison properties; compare an attributevalue of said search feature for each comparison property to saidaverage attribute value; and depict demonstrably said comparison of saidattribute value for each comparison property to said average attributevalue with a symbol that indicates whether said attribute value for eachcomparison property is one of above, below and substantially equal tosaid average attribute value.
 25. The article of claim 24 includinginstructions that, when applied to the machine, cause the machine tosearch said pool and select properties using an initial filteringcriteria based on at least one of said plurality of search features. 26.The article of claim 25 including instructions that, when applied to themachine, cause the machine to determine a price range of purchase price.27. The article of claim 26 including instructions that, when applied tothe machine, cause the machine to: determine an upper price value usinga seller price; and determine a lower price value using a purchaseprice.
 28. The article of claim 24 including instructions that, whenapplied to the machine, cause the machine to compare at least oneattribute of said properties to at least one of said plurality of searchfeatures.
 29. The article of claim 24 including instructions that, whenapplied to the machine, cause the machine to: sum said attribute valueof each comparison property into a sum; and divide said sum by a totalnumber of comparison properties to determine said average attributevalue.
 30. The article of claim 29 including instructions that, whenapplied to the machine, cause the machine to round said averageattribute value.
 31. The article of claim 24 including instructionsthat, when applied to the machine, cause the machine to select from thegroup consisting of property type, purchase price, location, buildingtype, light, space and cost.
 32. The article of claim 24 includinginstructions that, when applied to the machine, cause the machine todisplay said comparison in a grid.
 33. The article of claim 24 includinginstructions that, when applied to the machine, cause the machine todisplay said comparison in at least one of a bar chart and pie chart.34. The article of claim 24 including instructions that, when applied tothe machine, cause the machine to display the symbol selected from thegroup consisting essentially of ‘+’, ‘−’ and ‘=’ based on saidcomparison.